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Home >> Equality >> Multiply with same number >>

Multiply both sides of equality with same number

Add same number Add different number Subtract same number Subtract different number Multiply with same number
Multiply with different numbers Divide by same number Divide by different number

Explanation: When both the sides of equation i.e. L.H.S. and R.H.S of the equation are multiplied with same number, the equality still holds true.

Let’s understand it with the help of following examples:

Example 1 - Multiply both the sides of given equation with 10 and check what happens to equality
4 X 3 = 2 X 6

Solution - This proceeds as :
Add 5 to both sides of given equation and we get;
4 X 3 X 10 = 2 X 6 X 10

Solve L.H.S. and we get;
L.H.S. = 4 X 3 X 10
L.H.S. = 120

Solve R.H.S. and we get
R.H.S. = 2 X 6 X 10
R.H.S. = 120

Since L.H.S. = R.H.S i.e. 120 = 120

So the given equation 4 X 3 = 2 X 6, is said to be in equality even after multiplying both sides by 10 and hence we get
“When both the sides of equation i.e. L.H.S. and R.H.S of the equation are multiplied with same number, the equality still holds true.”


Example 2 - Multiply both the sides of given equation with 2 and check what happens to equality
3 + 3 = 5 + 1

Solution - This proceeds as :
Add 5 to both sides of given equation and we get;
(3 + 3) X 2 = (5 + 1) X 2

Solve L.H.S. and we get;
L.H.S. = (3 + 3) X 2
L.H.S. = 12

Solve R.H.S. and we get
R.H.S. = (5 + 1) X 2
R.H.S. = 12

Since L.H.S. = R.H.S i.e. 12 = 12

So the given equation 3 + 3 = 5 + 1, is said to be in equality even after multiplying both sides by 2 and hence we get
“When both the sides of equation i.e. L.H.S. and R.H.S of the equation are multiplied with same number, the equality still holds true.”

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